Our calculations were performed with the diffusion Monte Carlo (DMC)
method. This well-established technique allows us to solve exactly the
Schroedinger equation within some statistical errors to
obtain the ground state energy of a system of interacting
bosons [1]}.
This is exactly our case, since in its lowest energy state
(\(para\) -H\(_2\) ) the hydrogen molecule behaves as a boson. To apply
the DMC algorithm, we need the potentials to describe the H\(_2\) -H\(_2\) 
interaction (we chose the Silvera and Goldman expression [2]}, a
standard model for calculations involving \(para\) -H\(_2\) ), and the C-H\(_2\)  one.
For the latter, we used a Lennard-Jones potential with
parameters taken from
Ref. coleh2, as used previously to describe the phase
diagram of H\(_2\)  adsorbed on graphene [3]}. All the individual C-H\(_2\) 
pairs were considered, i.e., we took into consideration the corrugation effects
due to the real structure of the nanotube.
